Short production runs are common in enterprises that require a high degree of flexibility and variety in manufacturing processes. To date, past research on short production runs has little focus on the multivariate control charts. In view of this, fixed sample size (FSS) and variable sample size (VSS) Hotelling's T2 charts are designed to monitor the process mean when the production horizon is finite. Optimal parameters to minimize the out‐of‐control (1) truncated average run length (TARL) and (2) expected TARL (ETARL) are provided such that the in‐control TARL is equal to the number of inspections (say I). The numerical study considers the run length performances of the FSS and VSS T2 short‐run charts for both known and unknown shift sizes. The VSS T2 short‐run chart performs well in swiftly detecting various mean shifts in comparison with the FSS T2 short‐run chart. Additionally, the VSS T2 short‐run chart is superior to the FSS T2 short‐run chart, in terms of the truncated standard deviation of the run length, expected truncated standard deviation of the run length, probability that the chart signals an alarm within the I inspections, ie, P(I) and expected P(I). A case study on the impurity profile of a crystalline drug substance illustrates the implementation of the VSS T2 short‐run chart.

The standard deviation chart (S chart) is used to monitor process variability. This paper proposes an upper‐sided improved variable sample size and sampling interval (VSSIt) S chart by improving the existing upper‐sided variable sample size and sampling interval (VSSI) S chart through the inclusion of an additional sampling interval. The optimal designs of the VSSIt S chart together with the competing charts under consideration, such as the VSSI S and exponentially weighted moving average (EWMA) S charts, by minimizing the out‐of‐control average time to signal (ATS1) and expected average time to signal (EATS1) criteria, are performed using the MATLAB programs. The performances of the standard S, VSSI S, EWMA S, and VSSIt S charts are compared, in terms of the ATS1 and EATS1 criteria, where the results show that the VSSIt S chart surpasses the other charts in detecting moderate and large shifts, while the EWMA S is the best performing chart in detecting small shifts. An illustrative example is given to explain the implementation of the VSSIt S chart.

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The side sensitive group runs double sampling (SSGRDS) chart incorporates the control charting concepts of the side sensitive group runs (SSGR) and double sampling (DS) charts. The SSGRDS chart which combines the efficiency of its basic charts is an effective approach to increase the speed of mean shift detection. The performance of the SSGRDS chart, based on the average number of observations to signal (ANOS), median number of observations to signal (MNOS) and percentiles of the number of observations to signal (PNOS) is investigated in this paper. Based on the results obtained, it is found that the SSGRDS chart becomes more sensitive in detecting mean shifts with an increase in the size of the process mean shift. With the use of MNOS and PNOS to measure the performance of the SSGRDS chart, the entire run length distribution is considered and this leads to a more complete understanding of the performance of the chart. The findings in this paper will provide a clearer picture on the run length properties of the SSGRDS chart which will facilitate practitioners in using the chart.

The integration of the curtailment method with control charts considerably improves the detection speed by signaling an out-of-control condition prior to the inspection of the whole sample. To date, few research works have focused on the incorporation of the curtailment method to improve the performance of control charts. Thus, this paper incorporates the curtailment approach with the synthetic chart to propose a synthetic control chart with curtailment (Curt_Syn) for detecting upward shifts in the fraction nonconforming, p. We compared the newly developed Curt_Syn chart with the synthetic, exponentially weighted moving average (EWMA), cumulative sum (CUSUM), EWMA with curtailment (Curt_EWMA), and CUSUM with curtailment (Curt_CUSUM) charts. From an overall perspective, the results reveal that the Curt_Syn chart surpasses the synthetic chart by 38% under various conditions. For all p shifts, the Curt_Syn chart outperforms the CUSUM and EWMA charts. When the p shift is large, the Curt_Syn chart is superior to the Curt_CUSUM and Curt_EWMA charts. To demonstrate the implementation of the Curt_Syn chart, an illustrative example is provided.